A wave height spectral model for simulation of wave diffraction and refraction

A new directional wave height spectral model for simulating combined wave refraction and diffraction in coastal regions is developed in this study. Besides the wave refraction, which has been considered in most of the existing energy spectral models (e.g., the third generation ocean wave model by WAMDI GROUP, 1988), the wave diffraction is also included in the present model. In this model, the wave height density spectrum is expressed as the complex function that enables the partial representation of wave phase information, the crucial factor for the modeling of wave diffraction. The strength of the wave diffraction is then quantified by the additional diffusion terms with the imaginary number of diffusivity, the original form of which can be derived from the mild slope equation. The model has been validated against comprehensive case studies for both the regular waves and irregular waves. Numerical results are compared to the available analytical solutions and experimental data for the problems of wave diffraction, wave refraction, and combined wave refraction and diffraction. The overall performance of the model is excellent. The model is proven to be a useful tool to simulate the transient state of ocean waves in the coastal region where both wave refraction and diffraction are significant.